CHAPTER 2. VERTICAL STRUCTURE OF THE ATMOSPHERE Measurement

CHAPTER 2. VERTICAL STRUCTURE OF THE ATMOSPHERE Measurement

CHAPTER 2. VERTICAL STRUCTURE OF THE ATMOSPHERE Measurement of atmospheric pressure with the mercury barometer: vacuum Atmospheric pressure P = PA = PB = Hg gh h A B Mean sea-level pressure: P = 1.013x105 Pa = 1013 hPa = 1013 mb = 1 atm = 760 mm Hg (torr) SEA LEVEL PRESSURE MAP THIS MORNING (2/4/14, 15Z)

and the forecast: weather.unisys.com SEA-LEVEL PRESSURE CANT VARY OVER MORE THAN A NARROW RANGE: 1013 50 hPa Consider a pressure gradient at sea level operating on an elementary air parcel dxdydz: P(x) P(x+dx) Pressure-gradient force Vertical area dydz Acceleration dF ( P( x) P( x dx))dydz

1 dP dx For P = 10 hPa over x = 100 km, ~ 10-2 m s-2 100 km/h wind in 3 h! Effect of wind is to transport air to area of lower pressure dampen P On mountains, however, the surface pressure is lower, and the pressure-gradient force along the Earth surface is balanced by gravity: P(z+z) P-gradient gravity P(z) This is why weather maps show sea level isobars even over land; the fictitious sea-level pressure assumes an air column to be present between the surface and sea level MASS ma OF THE ATMOSPHERE Mean pressure at Earth's surface: 984 hPa

Radius of Earth: 6380 km ma 4 R 2 PSurface g 18 5.13 10 kg Total number of moles of air in atmosphere: ma Na 1.8 1020 moles Ma Mol. wt. of air: 29 g mole-1 = 0.029 kg mole-1

QUESTIONS 1. What is the fractional increase in volume of water-soluble aerosol particles when relative humidity increases from 90% to 95%? (assume that the particles are mainly water, so neglect the contribution of the solute to particle volume). Assuming that visibility degradation is proportional to the cross-sectional area of the particles, what is the resulting percentage decrease in visibility? 2. Why does it take longer to boil an egg in Denver than in Boston? CLAUSIUS-CLAPEYRON EQUATION: PH2O, SAT = f(T) PH2O,SAT (hPa) PH 2O , SAT 1 1 A exp[ B ( )] T To

T (K) A = 6.11 hPa B = - 5310 K To = 273 K VERTICAL PROFILES OF PRESSURE AND TEMPERATURE Mean values for 30oN, March Stratopause Tropopause Barometric law (variation of pressure with altitude) Consider elementary slab of atmosphere: P(z+dz) P(z) unit area P( z ) P( z dz ) a gdz

PM a a RT Ideal gas law: dP Mag dz P RT dP a g

dz hydrostatic equation Assume T = constant, integrate: P( z ) P(0)e z/H RT with scale height H 7.4 km (T 250 K) Mag Barometric law na ( z ) na (0)e z/H

P( z ) P( z H ) ; e P( z ) P ( z 5km) 2 Application of barometric law: the sea-breeze effect

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